Problem: John Doe has an n × m table. John Doe can paint points in some table cells, not more than one point in one table cell. John Doe wants to use such operations to make each square subtable of size n × n have exactly k points.

John Doe wondered, how many distinct ways to fill the table with points are there, provided that the condition must hold. As this number can be rather large, John Doe asks to find its remainder after dividing by 1000000007 (109 + 7).

You should assume that John always paints a point exactly in the center of some cell. Two ways to fill a table are considered distinct, if there exists a table cell, that has a point in one way and doesn't have it in the other.

Input

A single line contains space-separated integers n, m, k (1 ≤ n ≤ 100; n ≤ m ≤ 1018; 0 ≤ k ≤ n2) — the number of rows of the table, the number of columns of the table and the number of points each square must contain.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier. 

Output

In a single line print a single integer — the remainder from dividing the described number of ways by 1000000007 (109 + 7).

Examples

Input

5 6 1


Output

45

Note

Let's consider the first test case: 

<image> The gray area belongs to both 5 × 5 squares. So, if it has one point, then there shouldn't be points in any other place. If one of the white areas has a point, then the other one also must have a point. Thus, there are about 20 variants, where the point lies in the gray area and 25 variants, where each of the white areas contains a point. Overall there are 45 variants.

Solution (in JAVA):

Solution:
import java.io.BufferedWriter;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.Writer;
import java.math.BigInteger;
import java.util.InputMismatchException;

/**
 * Actual solution is at the top, in class Solver
 */
final public class Main implements Runnable {
	private static String[] args;

	public static void main(String[] args) {
		Main.args = args;
		new Thread(null, new Main(), "MyRunThread", 1 << 26).start();
	}

	@Override
	public void run() {
		long time_beg = -1;
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		if (args.length > 0 && args[0].equals("outside")) {
			time_beg = System.currentTimeMillis();
			try {
				inputStream = new FileInputStream("IO/in.txt");
//				outputStream = new FileOutputStream("IO/out.txt");
			} catch (Exception e) {
				System.err.println(e);
				System.exit(1);
			}
		} else {
			try {
//				inputStream = new FileInputStream("file_name");
//				outputStream = new FileOutputStream("file_name");
			} catch (Exception e) {
				System.err.println(e);
				System.exit(1);
			}
		}

		Solver s = new Solver();
		s.in = new InputReader(inputStream);
		s.out = new OutputWriter(outputStream);
		if (args.length > 0 && args[0].equals("outside")) {
			s.debug = new DebugWriter(s.out);
		}

		s.solve();
		s.out.close();

		if (args.length > 0 && args[0].equals("outside")) {
			s.debug.close();
			System.err.printf("*** Total time: %.3f ***\n", (System.currentTimeMillis() - time_beg) / 1000.0);
		}
	}
}

final class Solver {
	InputReader in;
	OutputWriter out;
	DebugWriter debug;

	public void solve() {
		n = in.readInt();
		m = in.readLong();
		int k = in.readInt();
		dp = new long[n + 1][k + 1];
		C = combinations(n + 1, MOD);
		pow = new long[n + 1][2];
		for (int i = 0; i < n + 1; ++i)
			for (int kk = 0; kk < 2; ++kk)
				pow[i][kk] = power(C[n][i], m / n + kk, MOD);

//		dp[0][0] = 1;
//
//		for (int left = 1; left <= n; ++left)
//			for (int kk = 0; kk <= k; ++kk)
//				for (int i = 0; i <= Math.min(n, kk); ++i) {
//					int count = (m % n >= left ? 1 : 0);
//					dp[left][kk] += pow[i][count] * dp[left - 1][kk - i] % MOD;
//					if (dp[left][kk] >= MOD) dp[left][kk] -= MOD;
//				}
//
//
//		out.printLine(dp[n][k]);

		ArrayFiller.fill(dp, -1);
		out.printLine(rec(n, k));
//		debug.printLine(dp);
	}

	long[][] pow;
	long[][] dp;
	long[][] C;

	final long MOD = 1000_000_000 + 7;

	long m;
	int n;

	long rec(int left, int k) {
		if (dp[left][k] != -1) return dp[left][k];
		if (left == 0) {
			if (k == 0) return dp[left][k] = 1;
			else return dp[left][k] = 0;
		}

		long res = 0;

		for (int i = 0; i <= Math.min(n, k); ++i) {
			int count = (m % n >= left ? 1 : 0);
			res += pow[i][count] * rec(left - 1, k - i) % MOD;
			if (res >= MOD) res -= MOD;
		}

		return dp[left][k] = res;
	}

	public final static long power(long value, long exponent, final long MOD) {
		long res = 1;
		while (exponent > 0) {
			if ((exponent & 1) == 1)
				res = (res * value) % MOD;
			exponent /= 2;
			value = (value * value) % MOD;
		}
		return res;
	}

	public final static long[][] combinations(int N, long MOD) {
		long[][] C = new long[N + 1][N + 1];

		for (int n = 0; n <= N; ++n) {
			C[n][0] = C[n][n] = 1;
			for (int k = 1; k < n; ++k) {
				C[n][k] = C[n - 1][k] + C[n - 1][k - 1];
				if (C[n][k] >= MOD) C[n][k] -= MOD;
			}
		}

		return C;
	}
}

final class InputReader {
	private boolean finished = false;

	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;

	public InputReader(InputStream stream) {
		this.stream = stream;
	}

	private int read() {
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}

	public int peek() {
		if (numChars == -1)
			return -1;
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				return -1;
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar];
	}

	public int readInt() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public long readLong() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public String readString() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	public static boolean isSpaceChar(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	private String readLine0() {
		StringBuilder buf = new StringBuilder();
		int c = read();
		while (c != '\n' && c != -1) {
			if (c != '\r')
				buf.appendCodePoint(c);
			c = read();
		}
		return buf.toString();
	}

	public String readLine() {
		String s = readLine0();
		while (s.trim().length() == 0)
			s = readLine0();
		return s;
	}

	public String readLine(boolean ignoreEmptyLines) {
		if (ignoreEmptyLines)
			return readLine();
		else
			return readLine0();
	}

	public BigInteger readBigInteger() {
		try {
			return new BigInteger(readString());
		} catch (NumberFormatException e) {
			throw new InputMismatchException();
		}
	}

	public char readCharacter() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		return (char) c;
	}

	public double readDouble() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		double res = 0;
		while (!isSpaceChar(c) && c != '.') {
			if (c == 'e' || c == 'E')
				return res * Math.pow(10, readInt());
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		}
		if (c == '.') {
			c = read();
			double m = 1;
			while (!isSpaceChar(c)) {
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, readInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				m /= 10;
				res += (c - '0') * m;
				c = read();
			}
		}
		return res * sgn;
	}

	public boolean isExhausted() {
		int value;
		while (isSpaceChar(value = peek()) && value != -1)
			read();
		return value == -1;
	}
}

final class OutputWriter {
	private final PrintWriter writer;

	public OutputWriter(OutputStream outputStream) {
		writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
	}

	public OutputWriter(Writer writer) {
		this.writer = new PrintWriter(writer);
	}


	public void print(Object... objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(Object... objects) {
		print(objects);
		writer.println();
	}

	public void printFormat(String format, Object... objects) {
		writer.printf(format, objects);
	}


	public void print(char[] objects) {
		writer.print(objects);
	}

	public void printLine(char[] objects) {
		writer.println(objects);
	}

	public void printLine(char[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(int[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(int[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(int[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(short[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(short[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(short[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(long[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(long[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(long[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(double[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(double[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(double[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(byte[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(byte[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(byte[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(boolean[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(boolean[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(boolean[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void close() {
		writer.close();
	}

	public void flush() {
		writer.flush();
	}
}

final class DebugWriter {
	private final OutputWriter writer;

	public DebugWriter(OutputWriter writer) {
		this.writer = writer;
	}

	private void printDebugMessage() {
		writer.print("debug:\t");
	}


	public void printLine(Object... objects) {
		flush();
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printFormat(String format, Object... objects) {
		flush();
		printDebugMessage();
		writer.printFormat(format, objects);
		flush();
	}


	public void printLine(char[] objects) {
		flush();
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(char[][] objects) {
		flush();
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}


	public void printLine(double[] objects) {
		flush();
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(double[][] objects) {
		flush();
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}


	public void printLine(int[] objects) {
		flush();
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(int[][] objects) {
		flush();
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}


	public void printLine(short[] objects) {
		flush();
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(short[][] objects) {
		flush();
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}


	public void printLine(long[] objects) {
		flush();
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(long[][] objects) {
		flush();
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}


	public void printLine(byte[] objects) {
		flush();
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(byte[][] objects) {
		flush();
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}


	public void printLine(boolean[] objects) {
		flush();
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(boolean[][] objects) {
		flush();
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}


	public void flush() {
		writer.flush();
	}

	public void close() {
		writer.close();
	}
}


abstract class ArrayFiller {
	// fill int array
	public final static void fill(int[] array, int value) {
		for (int i = 0; i < array.length; ++i)
			array[i] = value;
	}

	public final static void fill(int[][] array, int value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(int[][][] array, int value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(int[][][][] array, int value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(int[][][][][] array, int value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(int[][][][][][] array, int value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(int[][][][][][][] array, int value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	// fill short array
	public final static void fill(short[] array, short value) {
		for (int i = 0; i < array.length; ++i)
			array[i] = value;
	}

	public final static void fill(short[][] array, short value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(short[][][] array, short value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(short[][][][] array, short value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(short[][][][][] array, short value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(short[][][][][][] array, short value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(short[][][][][][][] array, short value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	// fill long array
	public final static void fill(long[] array, long value) {
		for (int i = 0; i < array.length; ++i)
			array[i] = value;
	}

	public final static void fill(long[][] array, long value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(long[][][] array, long value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(long[][][][] array, long value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(long[][][][][] array, long value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(long[][][][][][] array, long value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(long[][][][][][][] array, long value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	// fill double array
	public final static void fill(double[] array, double value) {
		for (int i = 0; i < array.length; ++i)
			array[i] = value;
	}

	public final static void fill(double[][] array, double value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(double[][][] array, double value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(double[][][][] array, double value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(double[][][][][] array, double value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(double[][][][][][] array, double value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(double[][][][][][][] array, double value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	// fill boolean array
	public final static void fill(boolean[] array, boolean value) {
		for (int i = 0; i < array.length; ++i)
			array[i] = value;
	}

	public final static void fill(boolean[][] array, boolean value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(boolean[][][] array, boolean value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(boolean[][][][] array, boolean value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(boolean[][][][][] array, boolean value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(boolean[][][][][][] array, boolean value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(boolean[][][][][][][] array, boolean value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	// fill byte array
	public final static void fill(byte[] array, byte value) {
		for (int i = 0; i < array.length; ++i)
			array[i] = value;
	}

	public final static void fill(byte[][] array, byte value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(byte[][][] array, byte value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(byte[][][][] array, byte value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(byte[][][][][] array, byte value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(byte[][][][][][] array, byte value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(byte[][][][][][][] array, byte value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	// fill char array
	public final static void fill(char[] array, char value) {
		for (int i = 0; i < array.length; ++i)
			array[i] = value;
	}

	public final static void fill(char[][] array, char value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(char[][][] array, char value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(char[][][][] array, char value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(char[][][][][] array, char value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(char[][][][][][] array, char value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(char[][][][][][][] array, char value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	// fill String array
	public final static void fill(String[] array, String value) {
		for (int i = 0; i < array.length; ++i)
			array[i] = value;
	}

	public final static void fill(String[][] array, String value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(String[][][] array, String value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(String[][][][] array, String value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(String[][][][][] array, String value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(String[][][][][][] array, String value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}

	public final static void fill(String[][][][][][][] array, String value) {
		for (int i = 0; i < array.length; ++i)
			fill(array[i], value);
	}
}